The Parametric Ordinal-Recursive Complexity of Post Embedding Problems

Post Embedding Problems are a family of decision problems based on the interaction of a rational relation with the subword embedding ordering, and are used in the literature to prove non multiply-recursive complexity lower bounds. We refine the construction of Chambart and Schnoebelen (LICS 2008) and prove parametric lower bounds depending on the size of the alphabet.Comment: 16 + vii page

How the obscuration-zone hypothesis affects fragmentation: Illustration with the cohesive-element method

The problem of fragmentation prediction is at the origin of various analytical models. Among them, we focus on the ones introducing the idea of obscured zones. They assume that when a crack initiates at a defect, a stress release wave propagates away from the crack and protects the region encompassed by the wave from any further crack initiation. In this paper, we show by the use of numerical simulations that this assumption is only valid at high strain rates. The limit of its accuracy is even pushed to higher strain rates when the fragmentation process becomes more complex, that is to say when crack propagation, bifurcation or coalescence together with wave reflections are implied. In these cases, fragmentation lasts longer than the time needed to completely obscure the whole specimen and the obscured zone theory for fragmentation appears inadequate. We use the cohesive-element method to describe the damage and failure of the material considere

Delay-active damage versus non-local enhancement for anisotropic damage dynamics computations with alternated loading

International audienceAnisotropic damage thermodynamics framework allows to model the concrete-like mate- rials behavior and in particular their dissymmetric tension/compression response. To deal with dynamics applications such as impact, it is furthermore necessary to take into account the strain rate effect observed experimentally. This is done in the present work by means of anisotropic visco-damage, by introducing a material strain rate effect in the cases of posi- tive hydrostatic stresses only. The proposed delay-damage law assumes no viscous effect in compression as the consideration of inertia effects proves sufficient to model the apparent material strength increase. High-rate dynamics applications imply to deal with wave prop- agation and reflection which can generate alternated loading in the impacted structure. In order to do so, the key concept of active damage is defined and introduced within both the damage criterion and the delay-damage evolution law. At the structural level, strain localization often leads to spurious mesh dependency. Three-dimensional Finite Element computations of dynamic tensile tests by spalling are presented, with visco-damage and either without or with non-local enhancement. Delay- damage, as introduced, regularizes the solution in fast dynamics. The location of the macro-crack initiated is found influenced by non-local regularization. The strain rate range in which each enhancement, delay-damage or non-local enhancement, has a regularizing effect is studied

Relating timed and register automata

Timed automata and register automata are well-known models of computation over timed and data words respectively. The former has clocks that allow to test the lapse of time between two events, whilst the latter includes registers that can store data values for later comparison. Although these two models behave in appearance differently, several decision problems have the same (un)decidability and complexity results for both models. As a prominent example, emptiness is decidable for alternating automata with one clock or register, both with non-primitive recursive complexity. This is not by chance. This work confirms that there is indeed a tight relationship between the two models. We show that a run of a timed automaton can be simulated by a register automaton, and conversely that a run of a register automaton can be simulated by a timed automaton. Our results allow to transfer complexity and decidability results back and forth between these two kinds of models. We justify the usefulness of these reductions by obtaining new results on register automata.Comment: In Proceedings EXPRESS'10, arXiv:1011.601

Anisotropic 3D delay-damage model to simulate concrete structures

International audienceHigh dynamic loadings lead to material degradation and structural failure. This is even more the case for concrete structures where the parts initially in compression break in ten- sion due to waves propagation and reflection. The dissymmetry of the material behavior plays a major role in such cases, dissymmetry mainly due to damage induced anisotropy. Loading induced damage is most often anisotropic and one proposes here to take advantage of such a feature to build a damage model for concrete, dissymmetric in tension and in compression, 3D, suitable for dynamic computations. A single 2nd order tensorial damage variable D is consid- ered with a damage law ensuring a damage rate proportional to the square of the positive part of the strain tensor. One focus in the present work on viscous regularizations for the anisotropic damage model proposed, regularizations of Norton-Perzyna type. Numerical examples of dy- namic failures illustrate the ability and the efficiency of the model to deal with 3D structures

How the obscuration-zone hypothesis affects fragmentation: Illustration with the cohesive-element method

The problem of fragmentation prediction is at the origin of various analytical models. Among them, we focus on the ones introducing the idea of obscured zones. They assume that when a crack initiates at a defect, a stress release wave propagates away from the crack and protects the region encompassed by the wave from any further crack initiation. In this paper, we show by the use of numerical simulations that this assumption is only valid at high strain rates. The limit of its accuracy is even pushed to higher strain rates when the fragmentation process becomes more complex, that is to say when crack propagation, bifurcation or coalescence together with wave reflections are implied. In these cases, fragmentation lasts longer than the time needed to completely obscure the whole specimen and the obscured zone theory for fragmentation appears inadequate. We use the cohesive-element method to describe the damage and failure of the material considered

Indentation induced damage in silicon nitride

Presenting the goals of my Ph.D. projec

Operf: Benchmarking the OCaml Compiler

International audienceWe present operf, a set of tools to benchmark the OCaml compiler, with both micro-benchmarks, for fast feedback during development, and macro-benchmarks, for results on a larger set of benchmarks

Tenderbake - A Solution to Dynamic Repeated Consensus for Blockchains

First-generation blockchains provide probabilistic finality: a block can be revoked, albeit the probability decreases as the block "sinks" deeper into the chain. Recent proposals revisited committee-based BFT consensus to provide deterministic finality: as soon as a block is validated, it is never revoked. A distinguishing characteristic of these second-generation blockchains over classical BFT protocols is that committees change over time as the participation and the blockchain state evolve. In this paper, we push forward in this direction by proposing a formalization of the Dynamic Repeated Consensus problem and by providing generic procedures to solve it in the context of blockchains. Our approach is modular in that one can plug in different synchronizers and single-shot consensus. To offer a complete solution, we provide a concrete instantiation, called {{Tenderbake}}, and present a blockchain synchronizer and a single-shot consensus algorithm, working in a Byzantine and partially synchronous system model with eventually synchronous clocks. In contrast to recent proposals, our methodology is driven by the need to bound the message buffers. This is essential in preventing spamming and run-time memory errors. Moreover, {{Tenderbake}} processes can synchronize with each other without exchanging messages, leveraging instead the information stored in the blockchain